Problema Solution
Joe works no more than 20 hours a week during the school year. He is paid $10 an hour tutoring geometry students and $7 an hour delivering pizzas for pizza hut. Even though he loves geometry, he wants to spend at least 3 hours but no more than 8 hours a week tutoring. Find Joe's maximum earning.
Answer provided by our tutors
let
x = the hours tutoring geometry
y = the hours delivering pizzas
Joe works no more than 20 hours a week
x + y <= 20
he wants to spend at least 3 hours but no more than 8 hours a week tutoring
3 <= x <= 8
the money he earns is
P = 10x + 7y
we need to find the maximum of P
we have the following constrains
x + y <= 20
3 <= x <= 8
y > = 0
by graphing we find the corners of the graph:
(3, 0), (8, 0), (3, 17) and (8, 12)
and then plug into maximization equation:
(3, 0): P = 10*3 + 0 = 30
(8, 0): P = 10*8 + 0 = 80
(3, 17): P = 10*3 + 7*17 = 149
(8, 12): P = 10*8 + 7*12 = 164
Joe's maximum earning is $164.